Fracture Modifier 2.79 Problem
Looks like there are 2 problems:

1) the object seems to be non-manifold, that means Voronoi + Boolean might fail there, resulting in those unwanted white shards at the element boundaries. You could try Voronoi+Bisect+Fill instead, but note the filling algorithm isnt reliable there. Means it could look odd in some places. (like missing inner faces).

2) the textured shading with blender internal might be buggy with FM as well. You could try to check the material view instead. And... due to the unwanted extra shards, the internal shard order of the FM object might get messed up (just a guess) and thus the texture assignment goes wrong then too. But if possible, could you share the blend file so I can take a look ?